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Everywhere I look, it is recited as a quasi-mantra that "segmented mirrors are much lighter than monolithic mirrors", and I can't manage to find an explanation anywhere no matter how hard I look. To me, getting a monolithic mirror and cutting it up should provide strictly no weight savings.

I get that it's not exactly "cutting up a monolithic mirror", and I understand that there are many other advantages to segmented mirrors, but where does this weight economy come from?

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  • $\begingroup$ Same applies to ceramic tiles and giant micriscope slides. $\endgroup$ Sep 22, 2023 at 19:41

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A telescope's precision mirror needs to be very large, to collect lots of light, and needs to be very precisely shaped. Holding that proper shape is based on the mirror's ability to resist stress on its physical structure. A paper-thin mirror would be wobbly, every bump and movement would make it ripple and blur the image. But the biggest challenge a mirror has to deal with on earth is trying not to bend under its own weight. Even with a cradle to hold the mirror, a small deviation can affect the whole telescope's performance.

And that's where smaller mirrors are useful, because the square-cube law comes into play. A mirror's mass (which creates most of the forces it needs to deal with) is based on the cube of its size, but its structural strength (what resists those forces) is related to the cross-section, which increases by only the square of the size. Or to put that another way, a small mirror needs less thickness to have the same resistance to deformation, which means less overall weight. The composite mirror can be thinner relative to its overall width.

In theory, a single large mirror could be made thinner by cutting away some of the "back" of the mirror and then supporting it in a cradle or other support structure instead of depending on its internal strength (and indeed single large mirrors usually do need a special support cradle). But if you're going to make your mirror thin enough that it can't really support itself, you might as well just slice the big thin mirror into easy-to-handle pieces and mount them in the support structure independently, and that's just what a composite mirror is.

The down-side to this is that you have to mechanically support the mirror segments and hold them in a very precise alignment, but even that is often a feature rather than a bug. For space telescopes like the JWST, a segmented mirror can stow for launch in a much smaller space and then deploy on-orbit, and any Hubble-like mirror aberrations can potentially be managed by adjusting the support structure instead of needing corrective lenses or a whole new mirror. For earthly telescopes, a segmented mirror with a clever control system can functionally "flex" during observation to counteract the effects of atmospheric distortions and other sources of error.

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    $\begingroup$ The Hubble mirror is 15 inches thick (38 cm), but it is mostly hollow. The "vision problem" was not related to the thickness nor gravity. The mirror was polished to the wrong shape. $\endgroup$
    – JohnHoltz
    Sep 22, 2023 at 16:45
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    $\begingroup$ I may have the information a bit wrong. Gravity sag was identified as the reason the problem wasn't detected in testing, but on looking into it more, it sounds like they said "we can't test the focal length because of gravity sag" rather than that the sag directly affected the grinding. $\endgroup$ Sep 22, 2023 at 17:34
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    $\begingroup$ They did test it, but the null corrector apparatus they used was incorrectly assembled. Other tests were done but disregarded because the faulty null corrector was assumed to be more accurate. ntrs.nasa.gov/citations/19910003124 $\endgroup$ Sep 22, 2023 at 20:15
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    $\begingroup$ @ChristopherJamesHuff Yes, that's the document I was looking at. I'm referring to A.5.b: "After the assembly of the OTA, tests were performed to assure proper focus position... However, the data were complicated by gravity sag because the OTA was mounted horizontally, and only the focus position was verified." $\endgroup$ Sep 22, 2023 at 20:54
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When creating a mirror, you need to take a block of glass and grind and polish it until it has the desired shape. For telescopes this is typically a parabolic shape. So The thickness of the slab of glass depends on the size of the mirror as you still need a finite thickness at the center while you only remove very little at the edges.

If you now create the same diameter telescope from a total of 7 segments, the same reasoning applies - but to each piece separately. Thus you can save a lot of weight in the glass the mirror's surface is vapour-deposited on. Of course you still need to correctly align the 7 elements with respect to eachother, but the overall weight including the support structure will be much less than a giant solid piece of glass.

A similar reasoning also applies if you do not manufacture your mirror from a slab of glass but other material.

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    $\begingroup$ So this assumes that you only remove material from the reflecting side of a cylinder. Could you not also remove material from the other side? $\endgroup$
    – David Cian
    Sep 22, 2023 at 14:27
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    $\begingroup$ One probably could. Though that means to touch the optical side with whatever tool you need to shape the rear side - something you don't want. still... the risk is increased. And you will still need the support then as you need for a segmented mirror - and you have the much bulkier mirror itself which is much more complicated to get right during production and handle for installation (but you know that) :) $\endgroup$ Sep 22, 2023 at 14:49
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    $\begingroup$ If you're going to do some complicated cutting on the mirror to remove material from the back, why not segment it while you're at it? And if you're going to do that, you should just plan it from the start and make a composite mirror instead of casting a big huge mirror and then cutting it apart. $\endgroup$ Sep 22, 2023 at 15:32
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    $\begingroup$ "When creating a mirror, you need to take a block of glass..." no you don't, you start by casting it in an approximation of the desired shape. en.wikipedia.org/wiki/Spin_casting_(mirrors) $\endgroup$ Sep 22, 2023 at 16:24
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    $\begingroup$ Spin casting just gets you an approximately parabolic hollow in the top surface of the mirror to save time. It's still a huge block of glass that you have to shape. $\endgroup$ Sep 22, 2023 at 17:50
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The bottom line is that an (active) support mechanism to hold a segment in the right position will be lighter than the (passive) glass required if the mirror were not segmented.

There have been precursors of this for a long time, in the form of local support mechanisms with counterweights that compensated for sag as the mirror was repositioned.

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  • $\begingroup$ Nice shot of the contact points between the actuators and mirror in a recently-posted video from Tom Scott at youtu.be/QqRREz0iBes?t=520 Basically, it's a tour of the telescopes in the Atacama Desert. $\endgroup$ Oct 5, 2023 at 17:43

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